Question

An Algebra 2 student solved the equation 2x + 4 = 5 using the following steps. Is the student's work correct? If not, explain the mistake. 2x + 4 = 5 log25 = x + 4 log 2/log 5 = x + 4 log 2/log 5 - 4 = x x ≈ -3.569

Answer 1

Wow! man what level is this maths :P

Answer 2

Lol its algebra 2 xD

Answer 3

and why is that genius taking logs @Crushshroom

Answer 4

I don't understand where each step starts and ends, and I don't understand your logs. What are the bases?

Answer 5

Logs and Exponents confuse me /.| hold on, im going back to the question

Answer 6

Bases is 10 @MaxwellSmart !

Answer 7

If no base is mentioned we assume it to be 10

Answer 8

\(2x + 4 = 5\)

What is the first step after the equation?

Answer 9

-4 right?

Answer 10

on both sides?

Answer 11

Is this the first step of the student's solution?

\(\log25 = x + 4 \)

Answer 12

its 2^x+4=5

Answer 13

@MaxwellSmart do you want to solve this

Answer 14

I give up.
I don't understand the steps you wrote above.
You need to use the equation editor or the draw tool.

Answer 15

@Crushshroom i'll do it for ya!

Answer 16

This is a waste of time to just figure out what the problem is.

Answer 17

Thank you ( : I appreciate the help

Answer 18

Okay well im sorry, first time using this site -.-

Answer 19

So u take logs on both sides first!
log2^x+4= log5
using the power rule of logs
x+4= log5/log2
x= 2.321....-4
x= -1.67....

Answer 20

Then do what I suggested. Use the equation editor or the draw tool.
You can also take a pic of your text and attach it.

After much discussion, you finally wrote the equation is
2^x + 4 = 5
I have a feeling that is still not it, and it is
2^(x + 4) = 5

or

\(\large 2^{x + 4} = 5\)

Answer 21

YES! I just figured out how to use te equation thing so ill write the next step

Answer 22

\[\log_{2}5=x+4 \]

Answer 23

log 2/log 5 = x + 4

Answer 24

log 2/log 5 - 4 = x

Answer 25

Hey @MaxwellSmart I think u are the right person to help him!

Answer 26

x ≈ -3.569

Answer 27

thats the answer and im a girl xD

Answer 28

If you guys cant figure it out its okay ^.^

Answer 29

I think this is what the problem states were the steps the student did.

\(\large 2^{x + 4} = 5\)

\(\large log_2{5} = x + 4 \)

\(\large \dfrac{\log 2}{\log 5} = x + 4\)

\(\large \dfrac{\log 2}{\log 5} - 4 = x\)

\(\large x \approx -3.569\)

Answer 30

It is rather hard

Answer 31

Yes :D

Answer 32

Omg youre amazing ( :

Answer 33

Ok, it only took half an hour to figure out what the problem is.

Answer 34

Let me copy that and number the steps.
Then we'll be able to discuss them.

Answer 35

1. \(\large 2^{x + 4} = 5\)

2. \(\large log_2{5} = x + 4 \)

3. \(\large \dfrac{\log 2}{\log 5} = x + 4\)

4. \(\large \dfrac{\log 2}{\log 5} - 4 = x\)

5. \(\large x \approx -3.569\)

Answer 36

In step 3 what did u do @MaxwellSmart

Answer 37

The above is not my solution.
The above is a copy if your problem showing the steps the student did.

Step 1 is the equation.
Step 2 is taking log base two of both sides. It is correct.

Answer 38

Okay, so step three is the error?

Answer 39

Yes @Crushshroom I get x= -.167

Answer 40

Step 3 shows the left side being divided by log 5.
This is the change of base conversion.
Notice the logs no longer have the little base 2.
They are now base 10.

Answer 41

I understand that. Thanks a ton ( :!!!!

Answer 42

Step 3 is the error.
The conversion was done incorrectly.

Answer 43

This is the correct change of base formula:

\(\large \log_b x = \dfrac{\log_c x}{\log_c b} \)

Answer 44

That means in step 3, if the log is to be changed to base 10 from base 2, it should read:

2. \(\log_2 5 = x + 4\) is correct

3. \(\dfrac{\log 5}{\log 2} = x + 4\) is the correct step 3. Now the logs are base 10.
Notice that the student did this step incorrectly bec he inverted the fraction.

Answer 45

Alright, I see that. Thanks!

Answer 46

You're welcome.